https://file.aiquickdraw.com/mathbot/file/1726461618365v2pmk11e.jpg

The equation to graph is:

\[
5x + 5y = 15
\]

### Steps to Graph the Equation:
1. **Simplify the equation**:
   Divide the entire equation by 5 to simplify:
   \[
   x + y = 3
   \]
   Now, we have the equation in a simpler form.

2. **Rewrite in slope-intercept form**:
   \[
   y = -x + 3
   \]
   This equation is in the form \(y = mx + b\), where:
   - \(m = -1\) is the slope (indicating a downward slope),
   - \(b = 3\) is the y-intercept (the point where the line crosses the y-axis).

3. **Plot the y-intercept**:
   - Start by plotting the point (0, 3) on the y-axis.

4. **Use the slope**:
   - The slope is -1, which means for every 1 unit you move to the right along the x-axis, move 1 unit down.
   - From the point (0, 3), move right 1 unit and down 1 unit to get the point (1, 2). Plot this point.

5. **Draw the line**:
   - Draw a straight line through the points (0, 3) and (1, 2), extending in both directions.

Would you like me to generate a graph for this equation?

### Follow-up Questions:
1. What is the importance of slope-intercept form in graphing linear equations?
2. How do you find the slope from a linear equation in standard form?
3. What does the y-intercept tell you about the graph of a linear equation?
4. Can you convert any linear equation into slope-intercept form?
5. How can you check if a point lies on the graph of a linear equation?

### Tip:
When graphing a linear equation, always start by identifying the y-intercept and the slope, as they provide a clear starting point and direction for the line.

Learn how to graph the linear equation 5x + 5y = 15 by simplifying to slope-intercept form. This problem involves key algebra concepts such as finding the slope and y-intercept and is suitable for students in Grades 8-10.

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